1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tigry1 [53]
3 years ago
15

verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that s

atisfy the conclusion . f(x)= x^3-2x^2-4x+2 . [ -2,2]
Mathematics
1 answer:
Ghella [55]3 years ago
4 0

The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:

<span><span>x1 </span>= 0.42801</span>

<span><span>x2 </span>= −1.51414</span>

<span><span>x3 </span>= 3.08613</span>


x1 and x2 are in the desired interval [-2, 2]

f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

where f'(x) = 0, and that is <span>x_1 = -0.66</span>

so we see that Rolle's theorem holds in our function.

You might be interested in
What is the second step in costructing congruent angles?
sattari [20]

Answer:

Given an angle formed by two lines with a common vertex, this page shows how to ... The above animation is available as a printable step-by-step instruction sheet, which can be ... This construction works by creating two congruent triangles

Step-by-step explanation:

3 0
3 years ago
Jada Elena and Lin walked a total of 37 miles last week. jada walked 4 more miles that elena, and Lin walked 2 more miles than j
MA_775_DIABLO [31]

Answer:

Jada walked 13\ miles

Elena walked 9\ miles

Lin walked 15\ miles

Step-by-step explanation:

Let

x----> total miles walked by Jada

y----> total miles walked by Elena

z----> total miles walked by Lin

we know that

x+y+z=37 -----> equation A

x=y+4 -----> y=x-4 ------> equation B

z=x+2 ------> equation C

Substitute equation C and equation B in equation A and solve for x

x+(x-4)+(x+2)=37

3x=37+2

3x=39

x=13\ mi

Find the value of y

y=13-4=9\ mi

Find the value of z

z=13+2=15\ mi

therefore

Jada walked 13\ miles

Elena walked 9\ miles

Lin walked 15\ miles

3 0
3 years ago
Help me worth 25 points
eimsori [14]
Your area is 37, hope this helps.
6 0
3 years ago
Evaluate the expression 2ab^3 + 6a^3 - 4ab^2 when a = 2 and b = 4.
Lady bird [3.3K]
The answer is A) 176 
4 0
3 years ago
(8b+12)+(3n+6)+(9b-4)
Bas_tet [7]

Answer:

17b+3n+14

Step-by-step explanation:

no any step

okk

finished

5 0
3 years ago
Read 2 more answers
Other questions:
  • How do you put 36/10 into a decimal?
    15·2 answers
  • In a study relating the degree of warping, in mm, of a copper plate (y) to temperature in °C (x), the following summary statisti
    6·1 answer
  • There is a negative correlation between the number of years in college and earnings.
    10·2 answers
  • Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour running on her exercise wheel and scratching at the co
    14·1 answer
  • Written assignment: answer these questions. 30 points for correct answer. hagd (may or may not do brainliest)
    9·1 answer
  • How do I solve these?​
    9·1 answer
  • Suppose Z3 = 24 - 22. Which quadrant contains z3?
    7·2 answers
  • Find the value of x for g(x) = -x + 5 when g(x) = 2.
    8·2 answers
  • Please help with these questions!
    13·1 answer
  • Model this equation using a visual model. <br> 4x + 8.46 = 2x + 15.62
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!